Computer Science Thesis Proposal

Friday, December 3, 2021 - 1:00pm to 2:30pm


In Person and Virtual ET Gates Hillman 8102 and Zoom



Monte Carlo Geometry Processing

This thesis proposal explores how core problems in PDE-based geometry processing can be efficiently and reliably solved via grid-free Monte Carlo methods. Modern geometric algorithms often need to solve Poisson-like equations on geometrically intricate domains. Conventional methods most often mesh the domain, which is both challenging and expensive for geometry with fine details or imperfections (holes, self-intersections, etc.). In contrast, grid-free Monte Carlo methods avoid mesh generation entirely, and instead just evaluate closest point queries. They hence do not discretize space, time, nor even function spaces, and provide the exact solution (in expectation) even on extremely challenging models. More broadly, they share many benefits with Monte Carlo methods from photorealistic rendering: excellent scaling, trivial parallel implementation, view-dependent evaluation, and the ability to work with any kind of geometry (including implicit or procedural descriptions). We develop a complete “black box” solver that encompasses integration, variance reduction, and visualization, and explore how it can be used for various geometry processing tasks. In particular, we consider several fundamental linear elliptic PDEs on solid regions of Rn. Overall, we find that Monte Carlo methods can significantly broaden the horizons of geometry processing, since they handle problems of size and complexity that are essentially hopeless for conventional methods.

Thesis Committee:
Keenan Crane (Chair)
Ioannis Gkioulekas
Matthew O’Toole
Gautam Iyer
Matt Pharr (Nvidia)

In Person and Zoom Participation. See announcement.

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Thesis Proposal